The 30-year-old will be replaced Matt Giteau, who has played most of career at centre, leaving the Australians without their first and second-choice scrum-halves for the tour.
Cordingley was set to be the first-choice number nine after regular scrum-half and skipper George Gregan decided to take a rest from international duties following a tough season.
But the Queensland player announced on Wednesday that he was still troubled by a persistent ligament injury and ruled himself out of the tour.
"I've given it two days and I'm still not moving the way I would like or with the confidence that I would like," he said after leaving the Wallabies training base in Coffs Harbour, New South Wales.
"It's progressed slowly with treatment but at the moment it's still about 70% and I had a choice to either push it and see if I got through the tour or stay behind and get the injury properly attended to before next season.
"I don't think I could get through the training load, let alone the four Tests," he added.
In the meantime, Cordingley's scrum-half understudy at the Queensland Reds Josh Valentine has been called into the squad to fight New South Wales number nine Brett Sheehan for the vacant position.